[Canada]

Signal way: Server keeps tokens of registered users cached. Client makes tokens of all the numbers it has, remembering the token -> number map for them. Client sends tokens to server, server returns the subset that matched. Client knows which numbers match. Making the token 10 bytes rather than 20 just saves bandwidth.

Silent Circle way: Server keeps hashes of registered users cached. Client hashes all the numbers it has, remembering the hash -> number map for them. Client sends a small number of the most significant bits of its hashes. Server treats this like a mask or wildcard search, returns all matches. Client knows which match, also gets hashes for other users they don't know. Sure, the client can reverse them, but the client could have probed for them anyway. The server maybe/probably doesn't learn enough to preimage what the client sent because of too many collisions. The downside is that the number of bits the client sends needs to be appropriate given the size of the database, though that can be mitigated by sharding by country code/area code/whatever.